Lecture contents - albany.edusoktyabr/NNSE618/NNSE618-L21-hetero... · NNSE 618 Lecture #21 ......
Transcript of Lecture contents - albany.edusoktyabr/NNSE618/NNSE618-L21-hetero... · NNSE 618 Lecture #21 ......
NNSE 618 Lecture #21
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Lecture contents
• Heterojunctions
– Types of heterostructures
– Electrostatics
– Current
– Isotype heterojunctions
NNSE 618 Lecture #21
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• Determine band discontinuities DEc and DEv
from difference in electron affinities:
• Determine the built-in voltage from the
difference in work functions.
• Draw the bands at for the appropriate
doping
• Determine Vn and Vp and xn and xp from the
solution of Poisson’s Equation using Full
Depletion Approximation with fi as a
boundary condition.
Heterojunction: Band lineup
Formation of P-n heterojunction
21 mmFpFni qqEEq fff
NNSE 618 Lecture #21
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Type I (Straddling Alignment)
• AlGaAs/GaAs
• GaSb/AlSb
• GaAs/GaP
Type II (Staggered)
• InP/Al0.48In0.52P
• InxGa1-xAs/GaxSbxAs
• AlxIn1-xAs/InP
Type III (broken gap)
• InAs/GaSb
Types of heterojunctions
From Shur, 2003
NNSE 618 Lecture #21
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Type I: AlGaAs/GaAs
Types of heterojunctions
-6
-5.5
-5
-4.5
-4
-3.5
-3
0 0.2 0.4 0.6 0.8 1
Al content
Ban
d E
nerg
y, eV
Conduction band
Valence band (-0.46x)
Type III : InAs/GaSb
NNSE 618 Lecture #21
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Band edges alignment
(From Tiwari and Frank, APL 1992)
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Junction barrier:
The same using valence band parameters
• Or combining the two, independent of the free
carrier concentrations:
p-N heterojunction: electrostatics
Flat-band diagram of a p-n heterojunctions
cnp
cpn
cFpFniNn
NnkTEEEq
0
0lnDf
vpcn
cpvn
ipin
advci
NN
NNkT
nn
NNkT
EEq ln
2ln
2
DDf
vpn
vnp
viNp
NpkTEq
0
0lnDf
if
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Depletion widths and band bending are
calculated similar to a p-n homojunction
by solving the Poisson equation:
p-N heterojunction: electrostatics
Band diagram of a n-P heterojunctions
ai
d
nn V
Nqx
f
12
ai
a
p
p VNq
x f2
apdn
dn
NN
N
with
tain VVV f 211
taip VVV f 21
nx px
NNSE 618 Lecture #21
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• Band discontinuities result in the abrupt
changes in carrier densities at the
heterojunction
• In homojunction, the carrier densities are
continuous
• Carrier jump scales as (e.g. for holes):
• If Vp=Vn when nNd = pNa then majority
carrier densities will be equal at the
interface, but this is rather special case.
P-n heterojunction: free carrier profiles
Free carrier densities in p-N heterojunction
From Harris, 2002
Free carrier densities in p-n homojunction
NNSE 618 Lecture #21
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Graded
Forward
• Diffusion of majority
carriers
• Traps & recombination
in depletion region
Reverse
• Drift of Minority
Carriers
• Traps & recombination
in depletion region
Currents in heterojunctions
Forward
Abrupt
Forward
• Thermionic emission
over abrupt barrier
Reverse
• Thermionic emission
over abrupt barrier
• Drift of Minority
Carriers
Direct bias: injection
Carrier injection is controlled by the energy
barriers. Majority carrier injection from the
wide bandgap material is favored (electrons
in the Figs.) because of the reduction of
barrier for electrons by DEc and increase of
barrier for holes by DEv .
Currents: major mechanisms
Mechanisms can change with bias and doping asymmetry
From Harris, 2002
NNSE 618 Lecture #21
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Under forward bias at the edge of depletion region:
Low level injection,
• majority carrier density is constant:
• minority carrier density
High level injection,
• Minority & majority carrier density ~ equal
By having most of the depletion region in the
widegap material, G-R in the depletion region
is ~Ni ,and therefore, significantly reduced
Current in heterojunctions
ta VVipp enpn 2
ta VV
a
ip e
N
nn
2
ap Np
ta VVipp enpn
2
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• Isotype N-n+ heterojunction in thermal
Equilibrium
The properties of such junctions are very important
in VCSELs because there can be as many as 60-70
of them in series!
• Isotype N-n heterojunction under “Forward”
bias (negative bias to N-side)
Barrier VN decreases with applied bias, greatly
increasing J2 while J1 remains relatively constant
(compare with injection from wide-bandgap
material).
• Isotype N-n heterojunction under “Reverse”
bias (Positive bias to N-side)
Barrier VN increases with applied bias, reducing J2
to zero while J1 remains relatively constant, hence
the reverse current “saturates”
• Current is mainly thermionic as in M-S.
Isotype heterojunction
From Harris, 2002
NNSE 618 Lecture #21
12 Simple edge-emitting semiconductor laser diode
• In principle, a simple p-n junction may operate as a laser. However, a
double-heterostructure (DHS) laser diode is much more effective.
Broad area DHS semiconductor laser
• Advantage: acts as a light guide in the lateral direction
• Would be disadvantage for an LED: re-absorption
• However, the absorption becomes the gain - is favorable for lasing !
• Favorable for lasing also are:
• Confinement of electrons and holes - efficient recombination
• Confinement of light can be further control in separate confinement
structures
From Ebeling, 1992
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Simple edge-emitting semiconductor laser diode
• In p-n homojunction concentration of carriers is determined by diffusion
length and injection current.
• Problem of carrier diffusion can be overcome by heterojunction barrier.
• for AlxGa0.7As barrier with x = 0.3 DEn & DEp >12kT,
• Carrier leakage is reduced
• Injection rate
inj
dn J
dt qd
d